This short communication discusses two alternate techniques to treat hanging nodes in a quadtree mesh. Both the techniques share similarities, in that, they require only boundary information. Moreover, they do not require an explicit form of the shape functions, unlike the conventional approaches, for example, as in the work of Gupta \cite{gupta1978} or Tabarraei and Sukumar \cite{tabarraeisukumar2005}. Hence, no special numerical integration technique is required. One of the techniques relies on the strain projection procedure, whilst the other is based on the scaled boundary finite element method. Numerical examples are presented to demonstrate the accuracy and the convergence properties of the two techniques.
The Modified Direct Method: an Approach for Smoothing Planar and Surface Meshes
修正的直接法（Modified Direct Method，MDM）是一种用于光滑平面和曲面网格的迭代网格光滑方法，它是在Balendran [1]提出的非迭代光滑方法的基础上发展起来的。当平滑平面网格时，对于三角形和四边形网格，MDM的性能实际上与拉普拉斯平滑的性能相同;然而，MDM优于三四边形网格的拉普拉斯平滑。在光滑曲面网格时，对于三角形、四边形和四边形为主的混合网格，在光滑过程中，所有网格单元的平均质量（MQ）总是增加，均方误差（MSE）总是减小;对于三角形为主的混合网格，三角形的质量总是下降，四边形的质量总是上升。算例表明，该方法对平面和曲面三角形、四边形和四边形网格都是收敛的。
Nonlinear Geotechnical Analysis Using a Polygonal Cell-Based Smoothed Finite Element Framework
College of Water Conservancy and Hydropower Engineering, Hohai University（河海大学水利水电学院）；PowerChina Kunming Engineering Corporation Limited（中国电建昆明工程有限公司）；College of Harbour, Coastal and Offshore Engineering, Hohai University（河海大学港口海岸与近海工程学院）
Comparison of Multigrid Algorithms for High-order Continuous Finite Element Discretizations
School of Computing, University of Utah（犹他大学计算学院）；Courant Institute of Mathematical Sciences, New York University（纽约大学柯朗数学科学研究所）；Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校计算工程与科学研究所）
Two-dimensional seepage analysis using a polygonal cell-based smoothed finite element method
PowerChina Kunming Engineering Corporation Limited（中国电建集团昆明工程有限公司）；College of Water Conservancy and Hydropower Engineering, Hohai University（河海大学水利水电学院）；College of Harbour, Coastal and Offshore Engineering（海岸与海洋工程学院）；Yunnan Institute of Water Resources and Hydropower Research（云南省水利水电研究院）
Goal-Oriented Adaptive Finite Element Multilevel Quasi-Monte Carlo
King Fahd University of Petroleum and Minerals（国王法赫德石油矿物大学）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；RWTH Aachen University（亚琛工业大学）
Learned Finite Element-based Regularization of the Inverse Problem in Electrocardiographic Imaging
Institute for Applied Mathematics, University of Bonn, Germany（波恩大学应用数学研究所）；Department of Mathematics and Scientific Computing, University of Graz, Austria（格拉茨大学数学与科学计算系）；Institute of Artificial Intelligence, Medical University of Vienna, Austria（维也纳医学大学人工智能研究所）；Heart Center Bonn, Department of Internal Medicine II, University Hospital Bonn, Germany（波恩心脏中心，波恩大学医院第二内科部）；Department of Mathematics, University of Trento, Italy（特伦托大学数学系）
